Question

Given the definitions of f(x) and g(2) below, find the value of (gof)(9). f(x) = -x +11 g(x) = 3x² - x + 14

Answer 1

The function f(x)=-x+11 and g(x)=3x^2-x.

The function gof(x) means that g(f(x)).

Determine the function gof(x).

$\begin{gathered} (\text{gof)(x)}=g(f(x)) \\ =3(-x+11)^2-(-x+11) \\ =3(x^2-22x+121)+x-11 \\ =3x^2-66x+363+x-11 \\ =3x^2-65x+352 \end{gathered}$

Substitute 9 for x in the equation to obtain the value of (gof)(9).

$\begin{gathered} (gof)(9)=3(9)^2-65(9)+352 \\ =3\cdot81-585+352 \\ =243-233 \\ =10 \end{gathered}$

So answer is 10.